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All results from a given calculation for S4 (Sulfur tetramer)

using model chemistry: wB97X-D/cc-pVTZ

19 10 17 12 22

States and conformations

State Conformation minimum conformation conformer description state description
1 1 no D2D 1A1
1 2 yes C2V 1A1
1 3 no D2H 1AG

Conformer 1 (D2D)

Jump to S1C2 S1C3
Energy calculated at wB97X-D/cc-pVTZ
 hartrees
Energy at 0K-1592.786483
Energy at 298.15K 
HF Energy-1592.786483
Nuclear repulsion energy351.203947
The energy at 298.15K was derived from the energy at 0K and an integrated heat capacity that used the calculated vibrational frequencies.
Vibrational Frequencies calculated at wB97X-D/cc-pVTZ
Mode Number Symmetry Frequency
(cm-1)
Scaled Frequency
(cm-1)
IR Intensities
(km mol-1)
Raman Act
4/u)
Dep P Dep U
1 A1 544 520 0.00 41.60 0.05 0.09
2 A1 202 193 0.00 2.35 0.75 0.85
3 B1 490 469 0.00 17.73 0.75 0.86
4 B2 306 293 0.00 8.26 0.75 0.86
5 E 465 445 0.00 4.44 0.75 0.86
5 E 465 445 0.00 4.44 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1235.8 cm-1
Scaled (by 0.956) Zero Point Vibrational Energy (zpe) 1181.5 cm-1
See section III.C.1 List or set vibrational scaling factors to change the scale factors used here.
See section III.C.2 Calculate a vibrational scaling factor for a given set of molecules to determine the least squares best scaling factor.
Rotational Constants (cm-1) from geometry optimized at wB97X-D/cc-pVTZ
ABC
0.11805 0.11805 0.06455

See section I.F.4 to change rotational constant units
Geometric Data calculated at wB97X-D/cc-pVTZ

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.429 0.309
S2 0.000 -1.429 0.309
S3 -1.429 0.000 -0.309
S4 1.429 0.000 -0.309

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.85802.11342.1134
S22.85802.11342.1134
S32.11342.11342.8580
S42.11342.11342.8580

picture of Sulfur tetramer state 1 conformation 1
More geometry information
Calculated Bond Angles
atom1 atom2 atom3 angle atom1 atom2 atom3 angle
S1 S2 S4 47.456 S1 S3 S4 47.456
S2 S1 S3 47.456 S2 S4 S3 47.456
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at wB97X-D/cc-pVTZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.000      
2 S 0.000      
3 S 0.000      
4 S 0.000      


Electric dipole moments
Electric dipole components in Debye
(What's a Debye? See section VII.A.3)
  x y z Total
  0.000 0.000 0.000 0.000
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -48.579 0.000 0.000
y 0.000 -48.579 0.000
z 0.000 0.000 -54.090
Traceless
 xyz
x 2.755 0.000 0.000
y 0.000 2.755 0.000
z 0.000 0.000 -5.511
Polar
3z2-r2-11.021
x2-y20.000
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 11.327 0.000 0.000
y 0.000 11.327 0.000
z 0.000 0.000 6.564


<r2> (average value of r2) Å2
<r2> 168.295
(<r2>)1/2 12.973

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at wB97X-D/cc-pVTZ
 hartrees
Energy at 0K-1592.797198
Energy at 298.15K 
HF Energy-1592.797198
Nuclear repulsion energy334.424074
The energy at 298.15K was derived from the energy at 0K and an integrated heat capacity that used the calculated vibrational frequencies.
Vibrational Frequencies calculated at wB97X-D/cc-pVTZ
Mode Number Symmetry Frequency
(cm-1)
Scaled Frequency
(cm-1)
IR Intensities
(km mol-1)
Raman Act
4/u)
Dep P Dep U
1 A1 693 662 7.59 27.43 0.14 0.25
2 A1 444 424 5.70 54.56 0.20 0.33
3 A1 137 131 0.36 14.49 0.43 0.60
4 A2 220 210 0.00 0.19 0.75 0.86
5 B2 659 630 154.92 4.05 0.75 0.86
6 B2 348 333 0.52 11.62 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1250.2 cm-1
Scaled (by 0.956) Zero Point Vibrational Energy (zpe) 1195.2 cm-1
See section III.C.1 List or set vibrational scaling factors to change the scale factors used here.
See section III.C.2 Calculate a vibrational scaling factor for a given set of molecules to determine the least squares best scaling factor.
Rotational Constants (cm-1) from geometry optimized at wB97X-D/cc-pVTZ
ABC
0.15887 0.07261 0.04983

See section I.F.4 to change rotational constant units
Geometric Data calculated at wB97X-D/cc-pVTZ

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.034 0.911
S2 0.000 -1.034 0.911
S3 0.000 1.600 -0.911
S4 0.000 -1.600 -0.911

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.06831.90783.2031
S22.06833.20311.9078
S31.90783.20313.2009
S43.20311.90783.2009

picture of Sulfur tetramer state 1 conformation 2
More geometry information
Calculated Bond Angles
atom1 atom2 atom3 angle atom1 atom2 atom3 angle
S1 S2 S4 107.268 S1 S3 S4 72.732
S2 S1 S3 107.268 S2 S4 S3 72.732
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at wB97X-D/cc-pVTZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.150      
2 S 0.150      
3 S -0.150      
4 S -0.150      


Electric dipole moments
Electric dipole components in Debye
(What's a Debye? See section VII.A.3)
  x y z Total
  0.000 0.000 1.661 1.661
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -50.949 0.000 0.000
y 0.000 -53.237 0.000
z 0.000 0.000 -48.369
Traceless
 xyz
x -0.146 0.000 0.000
y 0.000 -3.578 0.000
z 0.000 0.000 3.724
Polar
3z2-r27.448
x2-y22.288
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.765 0.000 0.000
y 0.000 18.896 0.000
z 0.000 0.000 11.763


<r2> (average value of r2) Å2
<r2> 201.053
(<r2>)1/2 14.179

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at wB97X-D/cc-pVTZ
 hartrees
Energy at 0K-1592.786476
Energy at 298.15K 
HF Energy-1592.786476
Nuclear repulsion energy339.992104
The energy at 298.15K was derived from the energy at 0K and an integrated heat capacity that used the calculated vibrational frequencies.
Vibrational Frequencies calculated at wB97X-D/cc-pVTZ
Mode Number Symmetry Frequency
(cm-1)
Scaled Frequency
(cm-1)
IR Intensities
(km mol-1)
Raman Act
4/u)
Dep P Dep U
1 Ag 763 729 0.00 35.23 0.21 0.34
2 Ag 309 295 0.00 47.51 0.25 0.40
3 Au 264 253 0.00 0.00 0.00 0.00
4 B1u 693 663 158.52 0.00 0.00 0.00
5 B2u 225i 215i 25.11 0.00 0.00 0.00
6 B3g 356 340 0.00 14.01 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1079.9 cm-1
Scaled (by 0.956) Zero Point Vibrational Energy (zpe) 1032.4 cm-1
See section III.C.1 List or set vibrational scaling factors to change the scale factors used here.
See section III.C.2 Calculate a vibrational scaling factor for a given set of molecules to determine the least squares best scaling factor.
Rotational Constants (cm-1) from geometry optimized at wB97X-D/cc-pVTZ
ABC
0.14858 0.08564 0.05433

See section I.F.4 to change rotational constant units
Geometric Data calculated at wB97X-D/cc-pVTZ

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.942 1.241
S2 0.000 0.942 -1.241
S3 0.000 -0.942 1.241
S4 0.000 -0.942 -1.241

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.48121.88383.1153
S22.48123.11531.8838
S31.88383.11532.4812
S43.11531.88382.4812

picture of Sulfur tetramer state 1 conformation 3
More geometry information
Calculated Bond Angles
atom1 atom2 atom3 angle atom1 atom2 atom3 angle
S1 S2 S4 90.000 S1 S3 S4 90.000
S2 S1 S3 90.000 S2 S4 S3 90.000
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at wB97X-D/cc-pVTZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.000      
2 S 0.000      
3 S 0.000      
4 S 0.000      


Electric dipole moments
Electric dipole components in Debye
(What's a Debye? See section VII.A.3)
  x y z Total
  0.000 0.000 0.000 0.000
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.269 0.000 0.000
y 0.000 -47.622 0.000
z 0.000 0.000 -52.627
Traceless
 xyz
x -1.145 0.000 0.000
y 0.000 4.326 0.000
z 0.000 0.000 -3.181
Polar
3z2-r2-6.363
x2-y2-3.647
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.729 0.000 0.000
y 0.000 12.305 0.000
z 0.000 0.000 17.500


<r2> (average value of r2) Å2
<r2> 186.828
(<r2>)1/2 13.669